This invention relates to a method for automatically correcting the systematic errors in measurement and manufacturing machines, which include machine tools and manipulators. The invention also relates to an apparatus for implementing the method.
Hereinafter, only machine tools will be considered for simplicity, however the same considerations with necessary adaptations are also valid for the other aforesaid machines.
In a machine tool the machining accuracy is known to depend on the precision of many elements along a path extending from the workpiece being machined and including the foundations, the machine itself and the tool, to form a ring which closes at the surface between the workpiece and the tool.
In a machine tool, the position of the tool relative to the workpiece is described by a theoretical mathematical model, hereinafter defined as the theoretical model, which provides the position and orientation of the tool in relation to the workpiece, on the basis of the position of the axes, assuming that no errors exist in the guide systems and that there is no structural yielding.
The theoretical model is complex to a greater or lesser extent, depending on the machine tool.
In the case of a paraxial machine with three axes, its theoretical model is very simple and consists essentially of three expressions, related to the reading of the respective axes.X1=C1−Co1X2=C2−Co2X3=C3−Co3
in which Xi (i=1, 2, 3) are the real coordinates of the tool within the prechosen reference system, Ci are the coordinates measured along the corresponding axes, and Coi are the zero positions.
With regard to the orientation of the spindle of a paraxial machine with three axes, the theoretical model provides constant angles.
On this basis, and focusing the description on a machine tool by way of example, the problem which this invention confronts and solves is to determine a mathematical model for said machine tool which is as close as possible to its real behaviour, to hence also take account of the causes of error, and to correct the consequent errors.
In a real machine tool the effective position and orientation of the tool in relation to the workpiece are a function of the position of each element relative to the position of the element which precedes it along the ring extending from the workpiece to the tool, so that the relative coordinates between the workpiece and tool and their relative orientation are a function of the reading of the machine axes, and also of many other quantities which take account of the errors present as far as possible.
In the case of a real machine tool with n axes in which many causes of error are present, with a determined applied tool its particular mathematical model is of typeX′1=f1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)X′2=f2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)X′3=f3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)α′1=g1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)α′2=g2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)α′3=g3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl)
in which Xi are the coordinates of the tool base in relation to the workpiece, Ci are the coordinates along the machine axes, Vi are physical variables causing errors, such as temperature and load, αi are the angles of orientation of the tool in relation to the workpiece, and fi and gi are functions of the machine mathematical model deriving from experience.
The aforestated expressions describe the position and orientation of the base of the final member, which in the case of a milling machine is the spindle cone.
The position and orientation of the final miller, consisting for example of the tool centre in the case of a spherical miller, can hence be deduced from the dimensions thereof in relation to the final member, i.e. from its three coordinates U, V, W, using the expressions:X1=X′1+V*α2−W*α3X2=X′2+W*α3−U*α1X3=X′3+U*α1−V*α2α′1=α1α′2=α2α′3=α3
obtaining that the position of the final point is always described by the following relationships which represent the mathematical modelX1=f1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)X2=f2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)X3=f3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)α1=g1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)α2=g2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)α3=g3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, U, V, W)
For a generic machine tool, in which all the parameters of the functions which relate position and orientation to the axis coordinates and to the physical variables have not yet been identified, the mathematical model is of parametric type and will be known as a parametric mathematical model as it also comprises the parameters Pi, and assumes a form of typeX1=f1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)X2=f2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)X3=f3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)α1=g1(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)α2=g2(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)α3=g3(C1, C2, . . . Ci, . . . Cn, V1, V2, . . . Vi, . . . Vl, P1, P2, . . . Pi, . . . Pm, U, V, W)in which Pi(i=1, 2, 3 . . . n) are m machine parameters, and U, V, W, are the tool dimensions.
When the parameters Pi have been identified and hence have assumed precise numerical values, the group of six expressions becomes the mathematical model of the machine tool.
For evident reasons of machining accuracy it is essential that this mathematical model of the machine tool is as close as possible to the real system, and hence reduces to a minimum all errors resulting from any difference between the position and orientation of the tool relative to the workpiece, as calculated from the mathematical model, and its real position.
Such errors are the result of errors in the mathematical model, which describes all the relative positions of all the component elements of the ring as heretofore described. In the particular case of a machine tool with three axes, these errors are due to:    errors between the workpiece surface and the surface of the worktable,    errors between the workpiece surface and the fixed reference system at the foundations,    errors between the reference system and the movable structure of the first axis,    errors between the movable structure of the first axis and the movable part of the second axis,    errors between the movable structure of the second axis and the movable structure of the third axis,    errors between the movable structure of the third axis and the head structure,    errors between the head and the spindle bush,    errors between the spindle bush and the tool cutting edge.
As the mathematical model of a machine tool is evidently more faithful the smaller the errors between the tool position indicated by the mathematical model and its real position, it is important that the parametric mathematical model contains, as far as possible, all the quantities and parameters which describe the position of the tool relative to the workpiece.
However, the more complicated the parametric mathematical model, the more difficult it is to define its parameter values and the more difficult it is to attain the desired precision.
In particular, identifying the mathematical model of the machine requires the use of instruments of various types (laser interferometers, electronic levels, etc.) which require continuous manual repositioning within the working field, with considerable time consumption.
Moreover the known correction systems do not enable the orientation of the final machine member to be corrected in relation to the errors provided by the mathematical model.
WO97/43703 already tackles the problem of automatically correcting the systematic errors in a machine tools, and solves it firstly by creating a parametric mathematical model of the machine tools and then by determining the numeric values of the single parameters, to obtain the mathematical model of the machine itself. According to this prior document, the determination of these parameters is obtained by submitting the parts of the machine to a series of movements and then of determining, by a series of measurements, the overall behaviour of the machine. These measurements comprise distance measurements carried out parallelly to the axes of the machine by means of laser interferometer but, in order to identify completely the mathematical model, they must be integrated by a series of measurements of other nature, carried out by specific apparatuses, such as telescopic ballbar, 5-D laser interferometer, spindle rotation error analyzer, dual-axis tilt analyzer, repeatability analyzer, autocollimator, compliance analyzer and spindle thermal growth analyzer. Consequently this method is very complex, it requires a lot of time (some months) for being carried out and also many instruments, by means of which skilled men can carry out a series of heteroaeneous measurements.